Transcendental properties of entropy-constrained sets: Part II
Mathematical Physics
2023-09-15 v2 math.MP
Quantum Physics
Abstract
In this work, we address the question of the impossibility of certain single-letter formulas by exploiting the semi-algebraic nature of various entropy-constrained sets. The focus lies on studying the properties of the level sets of relative entropy, mutual information, and R\'{e}nyi entropies. We analyze the transcendental structure of the set of states in which one of the aforementioned entropy quantities is fixed. Our results rule out (semi)algebraic single-shot characterizations of these entropy measures with bounded ancilla for both the classical and quantum cases.
Keywords
Cite
@article{arxiv.2302.09645,
title = {Transcendental properties of entropy-constrained sets: Part II},
author = {Vjosa Blakaj and Chokri Manai},
journal= {arXiv preprint arXiv:2302.09645},
year = {2023}
}
Comments
14 pages, 1 figure